Auto-Rig Pro Hand Rigging Issue
If you study the bones of a hand, you'll see that what we think of as the palm is really just the base of all the fingers connecting almost directly to the wrist. These bones should follow a similar structure.
I have literally just finished sorting out the hands in an auto-rig and this is what I had to do. This is in the step before you bind the rig.
In Edit Mode move each bone end to a knuckle or joint, near the top (the muscles are mostly underneath the fingers rather than uniformly surrounding the bone, and on top the bones are closer to the surface). Also it's a good idea to Ctrl +  R rotate each bone so that the Z axis goes through each joint, that way you won't get wonky gimbals after it's finished rigging.
Also check the rest of the rig this way to make sure everything is going to move as you want it to. Then hit Bind and it should be fine.